Motion blur is a natural effect when you film the world in
discrete time intervals. When a film is recorded at 25 frames
per second, each frame has an exposure time of up to 40 milliseconds
(1/25 seconds). All the changes in the scene over that entire 40
milliseconds will blend into the final frame. Without motion blur,
animation will appear to jump and will not look fluid.

When the frame rate of a movie is too low, your mind will no
longer be convinced that the contents of the movie are
continuous, and the movie will appear to jump (also called
strobing).

More information:

Wikipedia's
frame rate
article includes information about the history of frame rates, frame
rates in video games, etc.

Wikipedia's
rotary disk shutter
article includes information about the shutters used in motion
picture cameras.

RED Digital Cinema has an
excellent article
on the benefits of high frame rates (HFR), including sample videos
and discussion.

Film purists will criticize the lack of blur and strobing artifacts,
but all of our crew--many of whom are film purists--are now converts.
You get used to this new look very quickly and it becomes a much more
lifelike and comfortable viewing experience. It's similar to the
moment when vinyl records were supplanted by digital CDs. There's
no doubt in my mind that we're heading towards movies being shot and
projected at higher frame rates.